LMFDB - Space of modular forms of level 3600, weight 1, and Character 3600.e

Defining parameters

The following table gives the dimensions of various subspaces of $M_{1}(3600, [\chi])$.

The following table gives the dimensions of subspaces with specified projective image type.

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	6	0	0	0

Label	Dim.	$A$	Field	Image	CM	RM	Traces				$q$-expansion
Label	Dim.	$A$	Field	Image	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
3600.1.e.a	$1$	$1.797$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	$0$	$0$	$0$	$0$	$q+2q^{29}+2q^{41}+q^{49}-2q^{61}+2q^{89}+\cdots$
3600.1.e.b	$1$	$1.797$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1}) $	$\Q(\sqrt{3}) $	$0$	$0$	$0$	$0$	$q+2q^{13}-2q^{37}+q^{49}+2q^{61}+2q^{73}+\cdots$
3600.1.e.c	$2$	$1.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$	$q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
3600.1.e.d	$2$	$1.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$	$q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$

$ S_{1}^{\mathrm{old}}(3600, [\chi]) \cong $ $S_{1}^{\mathrm{new}}(144, [\chi])$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(400, [\chi])$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(900, [\chi])$$^{\oplus 3}$

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Label	Dim.	\(A\)	Field	Image	CM	RM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	Image	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
3600.1.e.a	\(1\)	\(1.797\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{5}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+2q^{29}+2q^{41}+q^{49}-2q^{61}+2q^{89}+\cdots\)
3600.1.e.b	\(1\)	\(1.797\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{3}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+2q^{13}-2q^{37}+q^{49}+2q^{61}+2q^{73}+\cdots\)
3600.1.e.c	\(2\)	\(1.797\)	\(\Q(\sqrt{-3}) \)	\(D_{6}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
3600.1.e.d	\(2\)	\(1.797\)	\(\Q(\sqrt{-3}) \)	\(D_{6}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)